Wednesday, May 30, 2012

D&D Next: The math behind advantages/distadvantages

There been a lot of talk over the new advantage/disadvantage system in D&D Next where instead bonuses you get to take the best of two rolls for an advantage and the worst of two rolls for disadvantages.

The math is straightforward

With an advantage you are looking for best of two results. To figure
out your odds you need to multiply the chance of FAILURE together to
find out the new chance of failure. For example if you need 11+ to hit
rolling two dice and taking the best means instead of a 50% of failing
you have only a 25% chance of failing (.5 times .5).

For a disadvantage where you take the worst of two dice roll you need
to multiply the chances of SUCCESS to find out the new odds. For
example if you need a 11+ to hit your chance success drops from 50% to
25% (.5 time .5).
Advantage 15+ to hit, goes from 25% chance of success to roughly 43% chance of success. (.75 time .75)
Disadvantage 15+ to hit, goes from 25% chance of success to roughly a 6% chance of success (.25 times .25)

The general rule of thumb that in the mid range of the d20 (from
success on a 9+ to 12+) advantage grant roughly a equivalent to a +5
bonus and disadvantage a -5 bonus. The increase and decrease in odds
tappers off when your odds of success approach 1 or 20. For example a
advantage on a 19+ your chance of success goes from 90% to 81% not quite
a +2 bonus on a d20.

An interesting property of the system is that there always a chance
of success and always a chance of failure. Unlike a modifier systems
where enough modifiers can mean auto success or auto failure. (Unless
you have a 20 is an automatic success and 1 a automatic failure)

A useful application of knowing the odds of rolling two dice is that
you can just covert it to a straight bonus when rolling for a large
number of NPCs. A bunch of goblins with an advantage from surprise that
need 13+ to hit the players you can just apply a +4 (or +5 if you round
up) bonus instead of rolling the second dice. This is because they have a
60% chance of failure on 13+. Taking .6 times .6 yields .36 a drop of
24%. Not quite a +5 bonus on a d20 dice.

If you really want to use criticals then compute the odds and factor that in. For example a critical of a natural 20 with advantage is 19+ on a single die. (.95 x .95 = .902 a +1 improvement on a d20).

I like this sort of mechanic. The first time I remember seeing it was in Barbarians of Lemuria, but they used it with a 2d6 base, rolling 3d6 keeping best/worst for ad/disad. Working that kind of probability math on a bell curve makes me itch, but I do like the feel of it enough to use the basic idea for my house ruled task resolution system in OD&D.

I think I prefer the +5/+2/-2/-5 modifiers of 4e. It allows you to differentiate between a big modifier and a small modifier. With advantage you always give a big modifier if they need an average roll and you always give a small modifier if they need a high or low roll. If somebody needs a 19 to hit and his opponent is blind, I want him to be able to get a +5 modifier rather than a +0.8 modifier. The flat modifiers may create autosuccess or autofailure. But it can only do that when the odds were going that way anyway. (and assuming you don't rule a 1 an autofailure and 20 an autosuccess.

Bat in the Attic Games

How to make a Sandbox

The Old School Renaissance

To me the Old School Renaissance is not about playing a particular set of rules in a particular way, the dungeon crawl. It is about going back to the roots of our hobby and seeing what we could do differently. What avenues were not explored because of the commercial and personal interests of the game designers of the time.

What are RPGs?

A game where the players play individual characters interacting with a setting with their actions adjudicated by a human referee.

Rules are an aide to help the referee adjudicate actions and to help the players interact with the setting.

Dice are used to inject uncertainty which make a tabletop RPG campaign more interesting than "Let's Pretend".

The only thing a player needs to do to roleplay a character is to act if he or she was really there in the setting in that situation.